Learning and Teaching Geometry: VideoCases for Mathematics Professional Development

Principal Investigator: 
Project Overview
Background & Purpose: 

The Learning and Teaching Geometry project (LTG) will create five video case modules focused on classroom instruction for use in professional development of middle school mathematics teachers. The materials will be designed to support teachers to develop an understanding of the mathematics knowledge for teaching the concept of similarity in geometry and beyond. Module I, the foundation module, will focus on a thorough grounding of similarity and will contain 6-8 video case sessions. The four extension modules (containing 3-4 video case sessions each) will offer options for further exploration on related topics depending upon teachers’ interests and needs.

Setting: 

This is a professional development materials project for middle school mathematics teachers.

Research Design: 

This project is designed to generate descriptive [case study, design research, observational] and causal [experimental] evidence. A videocase module for professional development is offered as an intervention. During the LTG field test in year three, HRI will conduct the full studies of implementation, teacher, and student learning. In each of 20 sites, two groups of at least five teachers each will be recruited. One group in each site will be randomly assigned to participate in professional development using the Foundation Module in year three; the other group will receive comparable PD in year four. This design provides a matched comparison group in year three, and an opportunity to follow specific sites and teachers in year four. The teachers who experience the Foundation Module in Year 3 will then experience at least one extension module during Year 4. HRI evaluators will administer implementation instruments to all sites, and also visit 8 sites to conduct observations and teacher participant interviews.

Instruments for measuring teacher learning will include both a multiple choice assessment of knowledge for teaching in geometry, and embedded assessment tasks in the LTG materials. The multiple choice assessment will be constructed from items developed by the Study of Instructional Improvement/Learning Mathematics for Teaching project at the University of Michigan (NSF #0335411) as an external measure of mathematics knowledge for teaching. Assessments embedded in the LTG materials, similar to those HRI developed for LTLF (Heck, 2003), also will be administered to examine teacher learning specific to key goals of the LTG materials. The measure of student performance will draw on geometry items from national assessments; it will consist of approximately 30 released items from the National Assessment of Education Progress and the Third International Mathematics and Science Study. Items will be selected that require students to use geometric reasoning appropriate to the middle and early high school grades. Teachers assigned to the Foundation Module in year 4 will complete pre- and post-PD administrations of the written assessment and the embedded assessments during year 4. Analyses indicate statistical power of approximately 0.82 for detecting a small to medium-sized effect on teacher learning. Variations in implementation will be explored as an explanatory factor for differences in teacher learning across sites. For the teachers who begin the PD in year 4, the assessment will be administered at the beginning and end of the 2010-2011 school year. Results will be compared using multi-level modeling, controlling for differences across classrooms and students’ beginning-of-year scores, in order to test for effects of teachers’ participation in LTG professional development. Statistical power for detecting a small to medium-sized effect is approximately 0.80. During year five, HRI will clean, transcribe, code and analyze data, and write a final summative report. Throughout the duration of the project, HRI will meet with staff to discuss specific objectives of the evaluation and findings and prepare annual reports addressing all evaluation activities and findings.

Findings: 

To date, this project has not yet generated findings.

Other Products: 

The Learning and Teaching Geometry project (LTG) will create five video case modules focused on classroom instruction for use in professional development of middle school mathematics teachers. The materials will be designed to support teachers to develop an understanding of the mathematics knowledge for teaching the concept of similarity in geometry and beyond. Module I, the foundation module, will focus on a thorough grounding of similarity and will contain 6-8 video case sessions. The four extension modules (containing 3-4 video case sessions each) will offer options for further exploration on related topics depending upon teachers’ interests and needs. The five modules are:

  1. Conceptualizing, Defining, and Representing Similarity (Foundation Module)
  2. Definitions and Theorems: What is the Difference?
  3. Similar or Merely Alike? The Role of Language in Geometry
  4. Choosing and Using Technological Tools to Enhance the Learning of Similarity
  5. From Inductive to Deductive Reasoning: Bridging to High School Geometry

Overall learning goals include supporting teachers (1) to understand links to congruence, isometries, and dilation, (2) to think of similarity in terms of scale factor—for strengthening proportional reasoning and generalizing about geometric measurement in 1,2, and 3 dimensions, and (3) to realize the essential role similarity of triangle plays in understanding linear functions and slope. These video case modules, consisting of 18-24 total video case sessions, will provide a coherent sequence of professional development materials that can be used within a variety of institutes and workshops for teachers. Each module will be comprised of two major sets of resources: (1) video case materials and (2) facilitation resources. Video case materials include video segments and other records from classroom lessons (e.g., samples of student work, teacher notes, and curriculum materials). Facilitation resources will provide support for the professional developers to use the video case materials with teachers (e.g., detailed agendas, mathematical commentaries, facilitation notes, and other resources that field test sites deem important).